Factors of 8
The factors of 8 are the numbers that divide 8 exactly without leaving any remainder. There are four factors of 8, they are 1, 2, 4, and 8. Hence, the highest factor is 8 that divides itself. If we add all the factors, then the sum will be equal to 15.
The pair factors of 8 are (1,8) and (2,4). These pair factors when multiplied together results in the original number. 8 is also a perfect cube, thus its prime factor will be a single digit. We can determine the factors of 8 by the division method and prime factorisation method.
What are the Factors of 8?
A number or an integer that divides 8 exactly without leaving a remainder, then the number is a factor of 8. As the number 8 is an even composite number, it has more than two factors. Thus, the factors of 8 are 1, 2, 4 and 8.
Pair Factors of 8
A pair of numbers, which are multiplied together resulting in an original number 8 is called the pair factors of 8. As discussed above, the pair factors of 8 can be positive or negative. The positive and negative pair factors of 8 is given below:
Positive Pair Factors of 8:
Positive Factors of 8 |
Positive Pair Factors of 8 |
1 × 8 |
(1, 8) |
2 × 4 |
(2, 4) |
Negative Pair Factors of 8:
Negative Factors of 8 |
Negative Pair Factors of 8 |
-1 × -8 |
(-1, -8) |
-2 × -4 |
(-2, -4) |
How to Find Factors of 8?
8 is a whole number that is also an even number. Since it is a single-digit number, therefore, it is much easier to find the factors of 8.
There are two methods to find the factors of 8:
- Division method
- Prime factorisation method
Factors of 8 by Division Method
The factors of 8 can be found using the division method. In the division method, we need to find the integers which divide 8 exactly without leaving a remainder, and those integers are considered as the factors of 8. Now, let us find the factors of 8 using the division method.
- 8/1 = 8 (Factor is 1 and Remainder is 0)
- 8/2 = 4 (Factor is 2 and Remainder is 0)
- 8/4 = 2 (Factor is 4 and Remainder is 0)
- 8/8 = 1 (Factor is 8 and Remainder is 0)
If we divide 8 by any numbers other than 1, 2, 8 and 8, it leaves a remainder. Hence, the factors of 8 are 1, 2, 4 and 8.
Prime Factorization of 8
The prime factorization of 8 is the process of writing the number as the product of its prime factors. Now, let us discuss the process of finding the prime factors of 8.
- Divide 8 by the smallest prime number, i.e. 2. 8/2 = 4
- Divide 4 by the smallest possible prime number, 4/2 = 2
- 2 is itself a prime number and is divisible by 2
- Therefore, the prime factorization of 8 is 2 × 2 × 2 or 2^{3}.
Another method to find the prime factors of 8 is the factor tree method.
Factor Tree
Hence, the number of prime factors of 8 is one. The prime factorisation of the whole number 8 is 2^{3}. The exponent in the prime factorisation is 3. When you add the number 1 with the exponent, i.e.,3 +1 = 4. Therefore, the number 8 has 4 factors.
Facts – Factors of 8
- Factors of 8 – 1, 2, 4 and 8
- Prime factorisation – 2 x 2 x 2
- Prime factor of 8 – 2
- Pair factors – (1,8) and (2,4)
- Sum of factors of 8 – 15
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Solved Examples on Factors of 8
Example 1:
Find the common factors of 8 and 5.
Solution:
The factors of 8 are 1, 2, 4 and 8.
The factors of 7 are 1 and 5.
As 5 is a prime number, the common factor of 8 and 5 is 1.
Example 2:
Find the common factors of 8 and 9.
Solution:
Factors of 8 = 1, 2, 4 and 8.
Factors of 9 = 1, 3, and 9.
Hence, the common factor of 8 and 9 is 1.
Example 3:
Find the common factors of 8 and 4.
Solution:
The factors of 8 are 1, 2, 4 and 8.
The factors of 4 are 1, 2 and 4.
Hence, the common factors of 8 and 4 are 1, 2, and 4.
Practise Questions on Factors of 8
- What is the lowest factor of 8?
- Is there any odd number that is a factor of 8?
- How many even numbers are the factors of 8?
Stay tuned with BYJU’S to know about factor 8 and the factors and prime factors of other numbers. Download BYJU’S – The Learning App to better experience and clarification.
Frequently Asked Questions on Factors of 8
What are the factors of 8?
The factors of 8 are 1, 2, 4 and 8.
What is the prime factorization of 8?
The prime factorization of 8 is 2 × 2 × 2 or 2^{3}.
What is the sum of all factors of 8?
What is the greatest common factor of 8 and 7?
What are the positive pair factors of 8?
The positive pair factors of 8 are (1, 8) and (2, 4).
Write down the negative pair factors of 8.
The negative pair factors of 8 are (-1, -8) and (-2, -4).
Is 2 a factor of 8?
Yes, 2 is a factor of 8. If 8 is divisible by 2, it leaves a quotient of 4 and remainder 0, and hence 2 is a factor of 8.